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# M5.3.7

Uses the intersection of two-dimensional figures (e.g., lines, triangles, squares) to derive geometric definitions such as parallel, perpendicular, Pythagorean theorem, and midpoint.

### Square Roots Using a Carpenter's Square

As demonstrated in a PUMAS example from Lin H Chambers, "How Now, Pythagoras", master carpenters regularly make practical use of geometry and, at times, the Pythagorean theorem in their craft. I found this out some time ago when a good friend told me how an old-time carpenter he worked with calculated square roots using a carpenter's square.

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### How Now, Pythagoras?

You may think of the Pythagorean theorem as useful only to geeky college freshmen who want to calculate how many steps they are saving by walking across the grass. Recently I learned of a very practical use of this theorem in a very unexpected place.

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### Geometry to the Rescue: A Story in Pictures

Our kitchen floor was in need of something (repair, replacement, rejuvenation?). This being the do-it-yourself age, we took ourselves to the nearest big box home store, and picked out a lovely laminate flooring in a pattern that looks like tile. The ads and the instructions all make it sound like a pretty simple project. We brought it home and set to work. Immediately, we ran into a problem (Fig. 1). Our breakfast nook is in an octagonal shape. This means no matter which wall we started on, we immediately had to tackle an angle cut.

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